We study a family of commuting selfadjoint operators $={\left({A}_{k}\right)}_{k=1}^{n}$, which satisfy, together with the operators of the family $={\left({B}_{j}\right)}_{j=1}^{n}$, semilinear relations ${\u2140}_{i}{f}_{ij}\left(\right){B}_{j}{g}_{ij}\left(\right)=h\left(\right)$, (${f}_{ij}$, ${g}_{ij}$, ${h}_{j}:{\mathbb{R}}^{n}\to \u2102$ are fixed Borel functions). The developed technique is used to investigate representations of deformations of the universal enveloping algebra U(so(3)), in particular, of some real forms of the Fairlie algebra ${U}_{q}^{\text{'}}\left(so\left(3\right)\right)$.

Let G be a Lie group and A(G) the Fourier algebra of G. We describe sufficient conditions for complex-valued functions to operate on elements u ∈ A(G) of certain differentiability classes in terms of the dimension of the group G. Furthermore, generalizing a result of Kirsch and Müller [Ark. Mat. 18 (1980), 145-155] we prove that closed subsets E of a smooth m-dimensional submanifold of a Lie group G having a certain cone property are sets of smooth spectral synthesis. For such sets we give an estimate...

The present article is a survey of known results on Schur and operator multipliers. It starts with the classical description of Schur multipliers due to Grothendieck, followed by a discussion of measurable Schur multipliers and a generalisation of Grothendieck's Theorem due to Peller. Thereafter, a non-commutative version of Schur multipliers, called operator multipliers and introduced by Kissin and Schulman, is discussed, and a characterisation extending the description in the commutative case...

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